Exercise 8 Page 849

The given solid is a prism. To calculate the surface area of a prism, we can use the known formula where

P

is the perimeter of the base,

h

is the height, and

B

is the area of the base.

S = P h + 2 B

The base of a cube is a square, this means that the base has four equal side lengths. Let's add them to find the perimeter of the base.

P P = s + s + s + s = 4 s

Now, we can calculate its area using the formula for area of a square.

B B = s \cdot s = s^{2}

Finally, we have enough information to find the length of a lateral edge of the cube. Let's substitute

S

with

294

square inches,

P

with

4 s,

h

with

s,

and

B

with

s^{2}

into the formula.

S = P h + 2 B

Substitute values

294 = (4 s) (s) + 2 (s^{2})

▼

Simplify right-hand side

294 = 4 s^{2} + 2 s^{2}

Add terms

294 = 6 s^{2}

$LHS / 6 = RHS / 6$

49 = s^{2}

$LHS = RHS$

7 = s

Rearrange equation

s = 7

The length of a lateral edge of a cube is

7 inches .